Innovation modelling and wavelet analysis of fractal processes in bio-imaging

Abstract

Growth and form in biology are often associated with some level of fractality. Fractal characteristics have also been noted in a number of imaging modalities. These observations make fractal modelling relevant in the context of bio-imaging. In this paper, we introduce a simple and yet rigorous innovation model for multi-dimensional fractional Brownian motion (fBm) and provide the computational tools for the analysis of such processes in a multi-resolution framework. The key point is that these processes can be whitened by application of the appropriate fractional Lapla-cian operator which has a corresponding polyharmonic wavelet. We examine the case of MRI and mammography images through comparison with theoretical results, which underline the suitability of fractal models in the study of bio-textures.